Related papers: Unitarity and unstable-particle scattering amplitu…
Sturmian theory for nucleon-nucleus scattering is discussed in the presence of all the phenomenological ingredients necessary for the description of weakly-bound (or particle-unstable) light nuclear systems. Currently, we use a macroscopic…
The method of factorization, based on the model of unstable particles with a smeared mass, is applied to the processes with an unstable particle in the intermediate state. It was shown, that in the framework of the method suggested, the…
Perturbative scattering amplitudes in gauge theories have remarkable simplicity and hidden infinite dimensional symmetries that are completely obscured in the conventional formulation of field theory using Feynman diagrams. This suggests…
In the context of quantum field theory (QFT), unstable particles are associated with complex-valued poles of two-body scattering matrices in the unphysical sheet of rapidity space. The Breit-Wigner formula relates this pole to the mass and…
One-dimensional quantum scattering from a local potential barrier is considered. Analytical properties of the scattering amplitudes have been investigated by means of the integral equations equivalent to the Schrodinger equations. The…
The symmetry energy coefficients, incompressibility, and single-particle and isovector potentials of clusterized dilute nuclear matter are calculated at different temperatures employing the $S$-matrix approach to the evaluation of the…
We show that the evaluation of scattering amplitudes can be formulated as a problem of multivariate polynomial division, with the components of the integration-momenta as indeterminates. We present a recurrence relation which, independently…
We study on-shell scattering amplitudes for continuous-spin particles (CSPs). Poincar\'e invariance, little-group $ISO(2)$ covariance, analyticity, and on-shell factorisation (unitarity) impose stringent conditions on these amplitudes. We…
We propose a simple, intuitive alternative method of deriving the rule for connecting asymptotic wave function amplitudes to scattering probabilities. This is illustrated using the standard example of a 1-D particle reflecting or…
We consider the inverse resonance problem in one-dimensional scattering theory. The scattering matrix consists of $2\times 2$ entries of meromorphic functions, which are quotients of certain Fourier transform. The resonances are expressed…
A non-unitary version of quantum scattering is studied via an exactly solvable toy model. The model is merely asymptotically local since the smooth path of the coordinate is admitted complex in the non-asymptotic domain. At any real…
Is string theory uniquely determined by self-consistency? Causality and unitarity seemingly permit a multitude of putative deformations, at least at the level of two-to-two scattering. Motivated by this question, we initiate a systematic…
We analyze the behavior of a non-Hermitian opened one-dimensional quantum system with $\mathcal{PT}$ symmetry. This system is built by a dimer, with balanced gains and losses described by a parameter $\gamma$. By varying $\gamma$ the system…
When massless particles are involved, the traditional scattering matrix ($S$-matrix) does not exist: it has no rigorous non-perturbative definition and has infrared divergences in its perturbative expansion. The problem can be traced to the…
We prove a lower bound for the modulus of the amplitude for a two-body process at large scattering angle. This is based on the interplay of the analyticity of the amplitude and the positivity properties of its absorptive part. The…
We consider a dual $S$-matrix Bootstrap approach in $d\geq 3$ space-time dimensions which relies solely on the rigorously proven analyticity, crossing, and unitarity properties of the scattering amplitudes. As a proof of principle, we…
We propose a partial answer to the question of what kind of ultrahigh-energy physics has to be taken into account to circumvent the appearance of ultraviolet divergencies; a more than sixty years old open question in quantum…
An effective field theory is used to give a model-independent description of Compton scattering at energies comparable to the pion mass. The amplitudes for scattering on the proton and the deuteron, calculated to fourth order in small…
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…
A consistent description of the results of the neutrino oscillation experiments carried out so far can be obtained from three basic properties of neutrinos and the parameters of the Hamiltonian matrix. Using these basic neutrino properties,…